Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Exercise Set - Page 196: 47

Answer

The function f is an odd function and is symmetric about the origin.

Work Step by Step

An odd function is the function having symmetry with the origin and an even function is the function having symmetry with the y-axis. To check whether the function is even or odd, substitute $-x$ in the place of $x$ in the function and simplify as follows: $\begin{align} & f\left( -x \right)=\left( -x \right)\sqrt{1-{{\left( -x \right)}^{2}}} \\ & f\left( -x \right)=-x\sqrt{1-{{x}^{2}}} \\ & f\left( -x \right)=-f\left( x \right) \end{align}$ On putting –x in the place of x, it can be seen that same function with opposite signs is obtained. Thus the definition of an odd function is fulfilled and the graph of the function is symmetric about the origin. Hence, the function is an odd function and the graph of the function is symmetric about the origin.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.